When a convex mirror of focal 'f' produces an image (1/n)th of the size of the object, then distance of the object from the mirror is what

magnification= focal length/focal length -object distance

m= f /(f - u) (1).

HERE,

m = +(1/n) ; f = +f ; u= – u . (since mirror is convex).

So, using those, equation (1) becomes,

(1/n) = f /(f+u)

or, (f+u)=nf

or, u = nf – f

or, u =(n – 1) f.